Method for encoding data

ABSTRACT

A method for encoding data includes a super cooling process wherein an input stream is manipulated, encoded and summarized to form entities that represent the input stream in a different form in super cooled sets. The super cooled sets can be used for example for the transmission and/or storage of the information contained within the input stream.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to the provisional applicationidentified by the U.S. Ser. No. 60/687,604, filed on Jun. 3, 2005, theentire content of which is hereby expressly incorporated herein byreference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

BACKGROUND OF THE INVENTION

In general, data encoding involves the process of representinginformation using fewer data units or bits than a more directrepresentation would require. While various algorithms and techniqueshave been developed for encoding data, there is a continuing need for aneffective and readily implemented encoding method. It is to suchmethods, and systems implementing the same, that the present inventionis directed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of a system for encoding data, which isconstructed in accordance with the present invention.

FIG. 2 shows a flow chart illustrating a general method for encodingdata in accordance with the present invention.

FIG. 3 is a flow chart illustrating one embodiment of a method forencoding data in accordance with the present invention.

FIGS. 4A-4Y cooperate to illustrate the method for encoding data for anexemplary input stream, more particularly.

FIG. 4A shows an exemplary input stream.

FIG. 4B shows an exemplary rippled input stream.

FIG. 4C shows an exemplary rotated rippled input stream generated in theformation of an exemplary source stream.

FIG. 4D shows the rotated rippled input stream of FIG. 4C with an addedend droplet so as to form the exemplary source stream.

FIG. 4E shows a formation of an exemplary encoded source stream from thesource stream of FIG. 4D.

FIG. 4F shows a formation of an exemplary series of source pucks fromthe exemplary encoded source stream of FIG. 4E.

FIG. 4G shows the series of source pucks from FIG. 4F.

FIG. 4H shows an exemplary rotated duplicate rippled stream generated inthe formation of an exemplary reverse stream.

FIG. 4I shows an exemplary reversed, rotated duplicate rippled streamgenerated in the formation of the exemplary reverse stream.

FIG. 4J shows the reversed, rotated duplicate rippled stream of FIG. 4Iwith an added end droplet so as to form the exemplary reverse stream.

FIG. 4K shows a formation of an exemplary encoded reverse stream fromthe reverse stream of FIG. 4J.

FIG. 4L shows a formation of an exemplary series of reverse pucks fromthe exemplary encoded reverse stream of FIG. 4K.

FIG. 4M shows the series of reverse pucks from FIG. 4L.

FIG. 4N shows an exemplary first group formed from a portion of theseries of source pucks of FIG. 4G and a portion of the series of reversepucks of FIG. 4M

FIG. 4O shows an exemplary second group formed from a portion of theseries of source pucks of FIG. 4G and a portion of the series of reversepucks of FIG. 4M.

FIG. 4P shows an exemplary first group bubble formed from the firstgroup of FIG. 4N.

FIG. 4Q shows an exemplary set of gum drop pairs formed from the firstgroup bubble of FIG. 4P.

FIG. 4R shows an exemplary set of gum drop pair types and counts for oddand even gum drop pairs of FIG. 4Q.

FIG. 4S shows an exemplary set of adjacent gum drop pairs formed fromthe first group bubble of FIG. 4P, and an exemplary set of adjacent gumdrop pairs types and counts for the adjacent gum drop pairs.

FIG. 4T shows an exemplary super cooled set for the first group of FIG.4N.

FIG. 4U shows an exemplary second group bubble formed from the secondgroup of FIG. 4O.

FIG. 4V shows an exemplary set of gum drop pairs formed from the secondgroup bubble of FIG. 4U.

FIG. 4W shows an exemplary set of gum drop pair types and counts for oddand even gum drop pairs of FIG. 4V.

FIG. 4X shows an exemplary set of adjacent gum drop pairs formed fromthe second group bubble of FIG. 4U, and an exemplary set of adjacent gumdrop pairs types and counts for the adjacent gum drop pairs.

FIG. 4Y shows an exemplary super cooled set for the second group of FIG.4O.

FIG. 5 shows a flow chart illustrating one embodiment of an encodingsubroutine for forming the series of source pucks in accordance with thepresent invention.

FIG. 6 shows one embodiment of a two tier encoding scheme.

FIG. 7 shows a flow chart illustrating one embodiment of an encodingsubroutine for forming the series of reverse pucks in accordance withthe present invention.

FIG. 8 shows an exemplary first group and an exemplary second grouphaving two inversion duets.

FIG. 9 shows a flow chart illustrating one embodiment of a groupingsubroutine for forming the first group and second group in accordancewith the present invention.

FIG. 10 shows a summarization subroutine for the gum drop pairs of thefirst group.

FIG. 11 shows a summarization subroutine for the gum drop pairs of thesecond group.

FIG. 12A shows a formation of an exemplary lock component and anexemplary key component for the first group in accordance with thepresent invention.

FIG. 12B shows an exemplary combination applied to the lock componentand the key component of FIG. 12A, and the resulting set of adjacent gumdrop pair types and count for the first group.

FIG. 13 shows a block diagram illustrating a frame constructed inaccordance with the present invention.

FIG. 14 shows an exemplary first group and second group having mirroredpucks.

FIG. 15 shows a double helix structure associated with an exemplarysubset of duets of the present invention.

FIG. 16A-16B cooperate to show application of one embodiment of atransformation process to the subset of duets of FIG. 20, moreparticularly:

FIG. 16A shows the transformation of the subset of duets into DNA pairs.FIG. 16B shows a flow chart illustrating the transformation process andthe transformation of an exemplary first duet as the transformationprocess is applied.

DETAILED DESCRIPTION OF THE INVENTION

The term “encoding”, and derivations thereof, as used herein generallyrefers to the process by which a set of data units are represented in adifferent form, for example for the purpose of storing or transmittingthe data units; and the term “decoding”, and derivations thereof, asused herein generally refers to the process of restoring a compressedset of data units to its normal or original form, for example for thepurpose of processing, displaying or otherwise using the data units.

Referring now to the drawings, and in particular to FIGS. 1 and 2. Shownin FIG. 1 and designated therein by a reference numeral 10 is a systemfor data encoding, and shown in FIG. 2 is a general method for dataencoding which is preformed by the system 10.

The novel encoding process of the present invention is referred toherein by the Applicant by the term “super cooling”. In general, duringthe super cooling process, a stream of data units, which is referred toherein as an “input stream”, is manipulated, encoded and summarized toform entities that represent the input stream in a different form. Thisrepresentative form of the original input stream is referred to hereinas “super cooled sets”. The super cooled sets can be used for examplefor the transmission and/or storage of the information contained withinthe input stream.

In one embodiment, the system 10 includes a control unit 18. The controlunit 18 can be any computational device capable of executing the supercooling process or logic. In one embodiment, the control unit 18executes a super cooling program contained in a storage device 20. Thestorage device 20, which can be for example a read-only memory device,stores the program code and commands required for operation by thecontrol unit 18 in performing the super cooling process on the inputstream. Alternately, the super cooling process may be incorporated intothe control unit 18 itself.

With reference now to FIG. 3, the operation of the control unit 18,i.e., the performing of the super cooling process, will now bedescribed. At a step 20, the control unit 18 receives or reads the inputstream. The input stream comprises a plurality of sequential binary dataunits or bits, i.e. 1's and 0's. The individual data units of the inputstream are generally referred to herein by the Applicant by the term“droplets.” For example, shown in FIG. 4A is an exemplary input streamwhich is used herein for purposes of discussion and clarity ofunderstanding, and to illustrate the various steps of the super coolingprocess to achieve the final super cooled sets (as shown in FIGS.4B-4Y). For the exemplary input stream of FIG. 4A, there are forty-fourdroplets.

Once the input stream is received, the control unit 18 branches to astep 22 where the length of the input stream is analyzed, and lengthenedif needed. To perform the super cooling process of the presentinvention, though not mandatory, it is advantageous for the total numberof droplets or length of the input stream to be an odd multiple of thenumber four (e.g., 3×4=12, 5×4=20, 11×4=44, etc.). Therefore, if theinput stream does not have a length that is an odd multiple of thenumber four, in the step 22 one or more data units or binary streamswhich Applicant refers to herein as “padding droplets,” or collectivelyas “after spray,” are concatenated or added to the end of the inputstream to meet this requirement. The values of the padding droplets arearbitrary, however the padding droplets have to be identified as beingextraneous to the input stream. For purposes of discussion and clarityof understanding, any padding droplets that are added to the inputstream are considered as part of the input stream in the discussion thatfollows. (Note that in the example shown in FIG. 4A, the exemplary inputstream contains forty-four droplets which is an odd multiple of four,and thus no padding droplets are required.)

Within the input stream, there is the possibility that there will be asequence of consecutive droplets which are repeated, i.e., which havethe same value. When there is a sequence of greater than three dropletsof the same value, the sequence is referred to herein as a “run.” Runscan negatively affect the super cooling process of the present inventionby causing ambiguities and anomalies. As such, it is desirable to breakup any runs that may exist in the input stream. Therefore, after thestep 22, the control unit 18 branches to a step 24, wherein additionaldroplets are introduced into the input stream in a pre-determinedsequence. This step 24 is referred to herein by the Applicant as“rippling” (or derivations thereof) and the additional droplets arereferred to herein as “ripple droplets.” Rippling of the input streamforms what is referred to herein as a “rippled input stream.”

There are different ways to perform the rippling step 24. In oneembodiment, the rippling step 24 comprises introducing a ripple dropletafter each consecutive input stream droplet, except the last droplet,wherein the ripple droplets are alternated in value as each rippledroplet is inserted into the input stream. In such an embodiment, therippling can be either “0-1 rippling” or “1-0 rippling.” For 0-1rippling, the first ripple droplet introduced is a zero, the secondripple droplet is a one, the third ripple droplet is a zero, and so on.For 1-0 rippling, the first ripple droplet introduced into the inputstream is a one, the second ripple droplet is a zero, the third rippledroplet is a one, and so on.

For example, shown in FIG. 4B is the exemplary input stream of FIG. 4Awith 0-1 rippling, which results in eighty-seven droplets. The firstfour ripple droplets in the rippled input stream of FIG. 4B areindicated by a downward arrow over each ripple droplet for purposes ofillustration.

Once the rippled input stream is achieved, the control unit 18 branchesto a step 28, wherein a duplicate of the rippled input stream isgenerated, which is referred to herein by the Applicant by the term“duplicate rippled stream”.

At this point, the rippled input stream and the duplicate rippled streamare each provided as an input to different sets of logic. The rippledinput stream will be discussed first for purposes of clarity ofunderstanding. However, it should be understood that the logic for therippled input stream and the logic for the duplicate rippled stream canbe performed in any order or simultaneously. In other words, it shouldbe understood that various steps of the super cooling process that lendthemselves to be performed in other orders or in parallel can beimplemented as such to shorten the execution time of the presentinvention.

For the rippled input stream, the control unit 18 branches to a step 32wherein the rippled input stream is “rotated to the right” such thateach of the droplets in the rippled input stream is shifted a positionto the right, and the right-most droplet is looped to or deposited inthe left-most position which is vacated. In one preferred embodiment,the rippled input stream is rotated to the right by N+1 droplets, whereN is the total number of droplets in the input stream (including anypadding droplets). As such, it can be seen that the relative ordering ofthe droplets is generally preserved, however the start (or first)droplet and the end (or last) droplet in the stream are different. Forexample, shown in FIG. 4C is the exemplary rippled input stream of FIG.4B rotated to the right by 44+1 or 45 droplets.

The control unit 18 then branches to a step 34, wherein a final enddroplet is added to the end of the rotated rippled input stream so as toform an even number of droplets. In one embodiment, the final enddroplet is set equal to the first droplet of the rotated rippled inputstream to make the total count of droplets even. For example, shown inFIG. 4D is the rotated rippled input stream of FIG. 4C with the finalend droplet having a value of “0” added at the end. The resulting streamof the steps 32 and 34 is referred to herein as a “source stream.”

It should be understood that while the super cooling process isdescribed in one embodiment as “rotating” droplets when forming thesource stream, the source stream can be equivalently generated bydefining a starting offset at which to begin forming the source streamfrom the droplets of the rippled input stream. If the first droplet inthe rippled input stream is considered to have an offset of zero, thenthe starting offset should be defined to be N−2, where N is the lengthof the input stream (including any padding droplets). For example, forthe rippled input stream of FIG. 4B, the starting offset would bedefined as 44−2 or 42. Therefore, the droplet at offset 42 (with thefirst droplet of the rippled input stream being at offset zero) would bethe first droplet of the source stream. Then the succeeding droplets ofthe rippled input stream would be put in the source stream until the endof the rippled input stream is reached, and then continue on to thebeginning of the rippled input stream until the droplet at offset 41 isreached. Then the final end droplet can be added to the end so as toform an even number of droplets in the source stream.

Once the source stream is generated in the steps 32 and 34, the controlunit 18 branches to an encoding subroutine, which shown in FIG. 3 as astep 36, wherein the droplets of the source stream are formed intorepresentative entities referred to herein by the Applicant by the term“pucks” or “drop pairs”. Because the pucks are formed from the sourcestream at this point, the pucks are more specifically referred to hereinby the Applicant by the term “source pucks.”

For purposes of clarity of understanding the scheme for formation of thepucks, an interim step is gone through in the encoding subroutine 36.The encoding subroutine 36 is shown in more detail in FIG. 5. In a step40 of the encoding subroutine 36, the control unit 18 takes twoconsecutive (side-by-side) and unique droplets in the source stream toform a pairing which is referred to herein as a “drop”, and then assignsto each drop a predetermined symbol according to the values of thedroplets in the drop. The plurality of encoded drops collectively forman encoded source stream comprising a plurality of symbols whichrepresent the droplets of the source stream.

The collective group of predetermined symbols used to encode the dropsof the source stream are referred to herein as a “drop code.” Since thedrops are formed from two consecutive droplets and the droplets arebinary in nature, there are four possible drop combinations: 00, 01, 10,and 11. In one embodiment, the first four letters of the alphabet arethe predetermined symbols, wherein the letter “A” is assigned to a drophaving the value 00; the letter “B” is assigned to a drop having thevalue 01; the letter “C” is assigned to a drop having the value 10; andthe letter “D” is assigned to a drop having the value 11.

For example, shown in FIG. 4E is the source stream of FIG. 4D whereinthe droplets of the source stream have been paired in groups of two toform drops (as indicated by a horizontal line under each drop) and thenthe encoded source stream resulting from application of the drop code toeach fo the drops (wherein each resulting encoded drop is indicated by avertical down arrow under its corresponding drop). The source stream isthereby converted from a binary stream to a quad stream.

While the predetermined symbols of the drop code have been describedherein as being A, B, C, and D by way of illustration, it should beunderstood by those skilled in the art that this particular designationis arbitrary and that any distinct letter or other symbol may be chosento represent one of the four drop combinations. For example, the lettersW, X, Y, Z; the letters A, C, G, T; the letters P, M, C, Q; the lettersG, K, A, R; etc., could be used to represent the four drop combinations.

Also, the present invention contemplates the utilization of twoequivalent types of encoding: “single tier” encoding and “two tier”encoding. It can be seen that the droplets of the rippled input streamcan be assigned as an “even” droplet or an “odd” droplet, depending onits position in the data stream. For example, if the first or leftmostdroplet is considered an even droplet, the next consecutive dropletwould be an odd droplet, and the next consecutive droplet would be aneven droplet, and so on. When the rippled input stream's even and odddroplets are taken together in one sequential series, or in one tier,when applying the drop code, as generally discussed above, the encodingis termed herein by the Applicant as single tier encoding. However, whenthe rippled input stream's even and odd droplets are separated into twoseries or tiers before applying the drop code, the encoding process istermed herein by the Applicant as two tier encoding.

To encode the two tiers, the drops are still formed by taking one evendroplet and one odd droplet (from the first and second tiers,respectively). However, two letters are assigned to each possiblecombination of droplets, i.e., 00, 01, 10, and 11. Then which of the twoletters to be assigned to a droplet is dependent on whether the encodingis being performed on the first tier or the second tier. For example,shown in FIG. 6 and taking the exemplary drop code discussed above of A,B, C and D, the possible combinations for two tier encoding is given.The first tier is encoded by assigning the value “00” (given by a “0”even droplet from the first tier and a “0” odd droplet from the secondtier) the letter “A”; while for encoding the second tier, the value “00”is assigned the letter “D”. For encoding the first tier, the value “01”(given by a “0” even droplet from the first tier and a “1” odd dropletfrom the second tier) is assigned the letter “B”; while for encoding thesecond tier, the value “01” is assigned the letter “C”. For encoding thefirst tier, the value “10” (given by a “1” even droplet from the firsttier and a “0” odd droplet from the second tier) is assigned the letter“C”; while for encoding the second tier, the value “10” is assigned the“B”. For encoding the first tier, the value “11” (given by a “1” evendroplet from the first tier and a “1” odd droplet from the second tier)is assigned the letter “D”; while for encoding the second tier, thevalue “11” is assigned the letter “A”.

As shown in FIG. 5, once the source code has been encoded, the controlunit 18 branches to a step 42 of the encoding subroutine 36. In the step42, the plurality of symbols of the encoded source stream are thenpaired to form a series of source pucks. As a result of the pairing,each source puck includes two consecutive symbols or drops of theencoded source stream. However, the symbols are not unique to only onesource puck. The series of source pucks include overlapping symbolsbetween adjacent source pucks in that a succeeding source puck in theseries of source pucks will included as its first (or left) drop thesecond (or right) drop of a preceding source puck; and each precedingsource puck will include as its second (or right) drop the first (orleft) drop of a succeeding source puck. Thus, it can be seen that thefirst puck in the series of source pucks (which does not succeed anothersource puck) will only have one “overlapping” drop (its right drop) withone other source puck in the series of source pucks; and the last puckin the series of source pucks (which does not precede another sourcepuck) will only have one “overlapping” drop (its left drop) with oneother source puck in the series of source pucks.

For example, shown in FIG. 4F is the encoded source stream of FIG. 4Ewherein the encoded drops of the encoded source stream have been pairedto form source pucks (as indicated by alternating horizontal lines belowthe pairings of encoded drops). The source pucks are further identifiedin FIG. 4F by an alphanumeric identifier having the prefix “SP” locatedunder each source puck. Also, for purposes of further discussion herein,each of the source pucks of FIG. 4F, and its corresponding alphanumericidentifier, is shown in series in FIG. 4G. As can be seen, the pairingstep 42 of the encoding subroutine 36 should result in an odd number ofsource pucks.

For the duplicate rippled stream discussed above, the control unit 18branches to a step 44, as shown in FIG. 3. In step 44, the duplicaterippled stream is “rotated to the left” such that each of the dropletsin the duplicate rippled stream is shifted a position to the left, andthe left-most droplet is looped to the right-most position which isvacated. The duplicate rippled stream is rotated to the left to the samedegree that the rippled input stream is rotated to the right duringformation of the source stream (e.g., by N+1 droplets). For example,shown in FIG. 4H is the duplicate rippled stream (which is a duplicateof the rippled input stream shown in FIG. 4B) which is rotated to theleft by 44+1 or 45 droplets.

The control unit then branches to a step 46, wherein the droplets of therotated duplicate rippled stream are reversed in order. For example,shown in FIG. 4I is the rotated duplicate rippled stream of FIG. 4Hwhich has been reversed in order. The droplets of the rotated duplicatedrippled stream can be reversed in order by rotating the droplets or bydefining a starting offset, in a similar manner as discussed above withreference to the source stream. The control unit 18 then branches to astep 48, wherein a final end droplet is added to the end of the rotatedand reversed duplicate rippled stream. In one embodiment, the final enddroplet is equal to the first droplet of the rotated and reversedduplicate rippled stream to make the total count of droplets even. Theresulting stream of the steps 44, 46 and 48 is referred to herein as a“reverse stream.”

Similar to the source stream, it should be understood that while thesuper cooling process is described in one embodiment as “rotating”droplets to form the reverse stream, the reverse stream can beequivalently generated by defining a starting offset at which to beginforming a pre-reversal stream from which the reverse stream isgenerated. If the first droplet in the duplicate rippled stream isconsidered to have an offset of zero, then the starting offset should bedefined to be N+1, where N is the length of the input stream (includingany padding droplets). For example, for the duplicate rippled streamwhich is duplicated from the rippled input stream of FIG. 4B, thestarting offset would be defined as 44+1 or 45. Therefore, the dropletat offset 45 (with the first droplet of the duplicate rippled streambeing at offset zero) would be the first droplet of the pre-reversalstream. Then the succeeding droplets of the duplicate rippled streamwould be taken in reverse order and put in the reversal stream until thebeginning of the duplicate rippled stream is reached, and then continueon to the end of the duplicate rippled stream until the droplet atoffset 45 is reached. This accomplishes the same end result to obtainthe reverse stream without the need to from the duplicate rippledstream, rotating it left and then reversing it.

Once the reverse stream is generated in the steps 44, 46 and 48, thecontrol unit 18 branches to an encoding subroutine, which is shown inFIG. 3 as a step 50. The encoding subroutine 50 for the reverse streamis similar to the encoding subroutine 36 discussed above with referenceto the source stream. Therefore, for purposes of brevity, the encodingsubroutine 50 for the reverse stream is discussed summarily below.

For purposes of clarity of understanding the scheme for formation of thepucks, an interim step is gone through in the encoding subroutine 50.The encoding subroutine 50 for the reverse stream is shown in moredetail in FIG. 7. At a step 52, the plurality of droplets of the reversestream are paired to form drops, and each drop is assigned apredetermined symbol according to the values of the droplets in the dropso as to form an encoded reverse stream comprising a plurality ofsymbols. Preferably, the drop code used to form the encoded reversestream is the same as the drop code used to form the encoded sourcestream (e.g. A, B, C, and D). For example, shown in FIG. 4K is thereverse stream of FIG. 4J wherein the droplets of the reverse streamhave been paired to form drops (as indicated by a horizontal line undereach drop) and then the encoded reverse stream resulting fromapplication of the drop code to each of the drops (wherein eachresulting encoded drop is indicated by a vertical down arrow under itscorresponding drop). The reverse stream is thereby converted from abinary stream to a auad stream.

Once the drops of the reverse stream are encoded, the control unit 18branches to a step 60 of the encoding subroutine 50, wherein theplurality of drops or symbols of the encoded reverse stream are pairedso as to form a series of pucks in a similar manner as discussed abovefor the formation of the source pucks. However, since the pucks areformed from the reverse stream in the steps 52 and 60, the pucks arespecifically referred to herein by the Applicant by the term “reversepucks.”

Each reverse puck includes two consecutive drops of the encoded reversestream, wherein the series of reverse pucks include overlapping dropsbetween adjacent reverse pucks in that a succeeding reverse puck in theseries of reverse pucks will include as its first (or left) drop thesecond (or right) drop of a preceding reverse puck, and each precedingreverse puck will include as its second (or right) drop the first (orleft) drop of a succeeding reverse puck. For example, shown in FIG. 4Lis the encoded reverse stream of FIG. 4K wherein the encoded drops ofthe reverse stream have been paired to form reverse pucks (as indicatedby alternating horizontal lines under the pairings of encoded drops).The reverse pucks are further identified in FIG. 4L by an alphanumericidentifier having the prefix “RP” located under each reverse puck. Also,for purposes of further discussion herein, each of the reverse pucks ofFIG. 4L, and its corresponding alphanumeric identifier, is shown inseries in FIG. 4M. As can be seen, the pairing step 60 of the encodingsubroutine 50 should also result in an odd number of reverse pucks(which is also equal to the number of source pucks in the series ofsource pucks).

It should be noted that every puck in the series of source pucks shownin FIG. 4G has two symbols which are different from each other exceptgenerally one, which is located about the middle of the series of sourcepucks. The same is true for the series of reverse pucks shown in FIG.4M. The source puck and the reverse puck which have two symbols that areequal or the same symbol are referred to herein by Applicant as an“inversion puck” or “middle puck.” For example, the inversion puck inFIG. 4G is the source puck identified by the alphanumeric identifier“SP22”, which has a value of CC, and the inversion puck in FIG. 4M isthe reverse puck identified by the alphanumeric identifier “RP23”, whichhas a value of BB.

It should be noted that while generally only one inversion puck willexist in the series of source pucks and in the series of reverse pucks,there are situations in which more than one inversion puck will exist inthe series of source pucks and in the series of reverse pucks, dependingon the number of droplets in the input stream. This is shown by way ofexample in FIG. 8, wherein the series of source pucks and the series ofreverse pucks shown therein have been formed in the manner discussedabove for another exemplary input stream, which is equivalent to onlythe first thirty-six droplets of the exemplary input stream shown inFIG. 4A.

It can be seen in FIG. 8 that in the series of source pucks, there arenow two inversion pucks, and in the series of reverse pucks there arenow two inversion pucks. To account for or anticipate for thepossibility of such occurrences, the super cooling process in oneembodiment assigns two pucks as inversion pucks, regardless of whetherthere are two pucks that have two symbols which are the same. When thereare two pucks, each of which have two symbols which are the same, thetwo pucks are assigned as the inversion pucks. For example, in FIG. 8,the two inversion pucks in the series of source pucks will be the sourcepucks labeled as “SP18” and “SP19”, and the two inversion pucks in theseries of reverse pucks will be the reverse pucks labeled as “RP18” and“RP19”. However, when only one puck exists which has two symbols whichare the same, which is referred to herein as a “true inversion puck”, itis assigned as one of the inversion pucks. Then for the series of sourcepucks, the source puck which succeeds the true inversion puck in theseries will be assigned as the second inversion puck for the series ofsource pucks. For the series of reverse pucks, the reverse puck whichprecedes the true inversion puck in the series will be assigned as thesecond inversion puck for the series of reverse pucks. For example, inFIG. 4G, the two inversion pucks will be the source puck labeled as“SP22” (which is the true inversion puck) and the source puck labeled as“SP23” which succeeds it; and in FIG. 4M, the two inversion pucks willbe the reverse puck labeled as “RP23” (which is the true inversion puck)and the reverse puck labeled as “RP22” which precedes it.

It can further be seen that when segments of the series of source pucksand segments of the series of reverse pucks are analyzed in aside-by-side comparison, there is a correspondence between the series ofsource pucks and the series of reverse pucks. In the comparison, each ofthe series of source pucks and the series of reverse pucks are firstseparated into two segments, which are referred to herein as a “tophalf” and a “bottom half.” The segments are generally formed about theinversion pucks. The top half of the series of source pucks includes theinversion pucks and the source pucks that precede the inversion pucks.The bottom half of the series of source pucks includes the inversionpucks and the source pucks that succeed the inversion pucks. Likewise,the top half of the series of reverse pucks includes the inversion pucksand the reverse pucks that precede the inversion puck, and the bottomhalf of the series of reverse pucks includes the inversion pucks and thereverse pucks that succeed the inversion pucks.

As shown for example in FIG. 4N, when the top half of reverse pucks ofFIG. 4M is grouped with the bottom half of the source pucks of FIG. 4Gtaken in reverse order so as to allow for a side-by-side comparison, itcan be seen that generally each reverse puck (with the exception of thefirst reverse puck) in the top half of reverse pucks has a value whichis the reverse of the value of a source puck located in a precedingposition in the reverse ordered, bottom half of source pucks. (Theprecedential relationship between the reverse pucks in the top half ofreverse pucks and the source pucks in the reverse ordered, bottom halfof source pucks is indicated in FIG. 4N by slanted lines drawntherebetween). In other words, it can be seen that the symbols of eachreverse puck represents binary values which are the reverse of thebinary values represented by the symbols of the correspondingprecedential source puck.

Consider for example the embodiment discussed above wherein the dropcode utilized to generate the source pucks and reverse pucks includedthe symbol A to represent the binary values 00. Those values in reverseare still 00 and therefore the symbol A would again be used to representthat reversal of values. Likewise, the symbol D represents the binaryvalues 11. Those values in reverse are still 11 and therefore the symbolD would again be used to represent that reversal of values. However, thesymbol B represents the binary values 01. Those values in reverse arenow 10 and therefore a different symbol, symbol C, would be used torepresent that reversal of values. Likewise, the symbol C represents thebinary values 10. Those values in reverse are now 01 and therefore adifferent symbol, symbol B, would be used to represent that reversal ofvalues.

Now in the case of the pucks, if for example the reverse puck includesthe symbols AD, which represents 0011 (as for RP2), the correspondingpreceding source puck represents the reverse of those binary valueswhich is 1100 or the symbols DA (as for SP43). As another example, ifthe reverse puck includes the symbols DC, which represents 1110 (as forRP3), the corresponding preceding source puck represents the reverse ofthose binary values, which is 0111 or the symbols BD (as for SP42). Asyet another example, if the reverse puck includes the symbols CB, whichrepresents 1001 (as for RP4), the corresponding preceeding puckrepresents the reverse of those binary values, which is 1001 or thesymbols CB (as for SP41).

Likewise, there is also a reverse correspondence between the “top half”of the source pucks and the “bottom half” of the reverse pucks taken inreverse order. In other words, when the top half of the source pucks andthe bottom half of the reverse pucks taken in reverse order are groupedtogether and analyzed in a side-by-side comparison, a reversecorrespondence exists in that the symbols of each source puck representsbinary values which are the reverse of the binary values represented bythe symbols of a corresponding precedential reverse puck. For example inFIG. 4O is the top half of source pucks of FIG. 4G grouped with thebottom half of the reverse pucks of FIG. 4M taken in reverse order. (Theprecedential relationship between the source pucks in the top half ofsource pucks and the reverse pucks in the reverse ordered, bottom halfof reverse pucks is indicated in FIG. 4O by slanted lines drawntherebetween).

To exploit these reverse relationships, the control unit 18 branches toa grouping subroutine, which is shown in FIG. 3 as a step 64, whereinthe series of source pucks resulting from the step 36 and the series ofreverse pucks resulting from step 50 discussed above are segmented,reordered and grouped to form a first group and a second group.

The grouping subroutine 64 is shown in more detail in FIG. 9. In thegrouping subroutine 64, the control unit branches to a step 70, whereinthe inversion pucks are located within the series of source pucks byidentifying at least one source puck in the series of source puckshaving two symbols which are equal or the same, as discussed above. Thecontrol unit 18 then branches to a step 72, wherein the series of sourcepucks are segmented generally about the inversion pucks so as to form atop segment of source pucks (also referred to herein as a “firstsegment”) and a bottom segment of source pucks (also referred to hereinas a “second segment”). The top segment of source pucks includes theinversion pucks and all the source pucks that precede the inversionpucks in the series of source pucks. The bottom segment of source pucksincludes the inversion pucks and the source pucks that succeed theinversion pucks in the series of source pucks.

Likewise for the series of reverse pucks, the control unit 18 in a step74 locates the one or more inversion pucks within the series of reversepucks by identifying at least one reverse puck in the series of reversepucks having two symbols that are equal or the same, in a manner asdiscussed above. The control unit 18 then branches to a step 76, whereinthe series of reverse pucks are segmented generally about the inversionpucks to form a top segment of reverse pucks (also referred to herein asa “third segment”) and a bottom segment of reverse pucks (also referredto herein as a “fourth segment”). The top segment of reverse pucksincludes the inversion pucks and the reverse pucks that precede theinversion puck in the series of reverse pucks. The bottom segment ofreverse pucks includes the inversion pucks and the reverse pucks thatsucceed the inversion pucks in the series of reverse pucks.

Although the grouping subroutine 64 is discussed above in terms of thesteps 70 and 72 and then the steps 74 and 76, it should be understoodthat the steps 70 and 72 can be preformed subsequent to orsimultaneously with the steps 74 and 76.

Once the source pucks and the reverse pucks have been segmented in thesteps 72 and 76, respectively, the control unit branches to a step 78 ofthe grouping subroutine 64, wherein the top segment of reverse pucks isgrouped with the bottom segment of source pucks taken in reverse orderto form the first group; and the top segment of source pucks is groupedwith the bottom segment of reverse pucks taken in reverse order to formthe second group. (See FIGS. 4N and 4O for an exemplary first group andan exemplary second group, respectively, which results from the seriesof source pucks of FIG. 4G and the series of reverse pucks of FIG. 4M.)

Once the first group and second group are formed in the step 64, thecontrol unit 18 at this point utilizes the first group and the secondgroup as an input to different sets of logic, although the sets of logicare similar. The first group will be discussed first for purposes ofclarity of understanding. However, it should be understood that thelogic for the first group and the logic for the second group can beperformed in any order or simultaneously.

As shown in FIG. 3, after the first group is formed in step 64, thecontrol unit 18 branches to a step 82, wherein the source pucks and thereverse pucks in the first group are reordered to form an orderingreferred to herein as a “first group bubble.” In general, the process ofreordering the source pucks and reverse pucks is referred to herein bythe Applicant by the term “bubbling” or derivations thereof. To bubblethe first group to form the first group bubble, the first reverse puckin the top segment of reverse pucks is assigned to a first entry of thefirst group bubble, followed by a plurality of entries comprisingpairings of each succeeding reverse puck in the top segment of reversepucks with its corresponding precedential source puck in the reverseordered, bottom segment of source pucks. This operation is morespecifically referred to as “Right/Left” bubbling.

Each of the reverse relationship pairings resulting from the bubblingstep 82 is referred to herein by the Applicant by the term “duet.” Thefinal duets or last entries of the first group bubble, which includesthe pairings of the inversion pucks in the top segment of reverse pucksand the inversion pucks in the reverse ordered bottom segment of sourcepucks, are referred to herein as “inversion duets.” For example, shownin FIG. 4P is an exemplary first group bubble resulting from thebubbling of the first group of FIG. 4N in a manner as discussed above.The first reverse puck (RP1) is given as BA, which is followed by aplurality of duets starting with AD-DA (RP2-SP43), DC-BD (RP3-SP42),CB-CB (RP4-SP41), and so on. The last two entries of the first groupbubble are the inversion duets AB-CA (RP22-SP23) and BB-CC (RP23-SP22).(Note that the duets, as well as other combinations of pucks, are shownand discussed herein with a “-” placed therebetween for purposes ofvisual clarity, and the “-” generally has no other value or significancewith regards thereto).

It can be seen that the first reverse puck in the first group bubble isnot paired in a duet. This first unpaired puck is referred to herein bythe Applicant by the term “bubble scum.” The set of duets following thebubble scum, with the exclusion of the inversion duets, is referred toherein by the term “bubble core.”

The adjacent pucks in adjacent duets in the bubble core in a sense“glue” the pucks together and when taken in the correct order in thebubble, substantially define the original input stream. Therefore, aspart of the super cooling process, they are paired together in step 82to form a plurality of entities referred to by the Applicant as “gumdrop pairs” or “gum pucks”. In other words, the gum drop pairs arepairings of adjacent pucks in adjacent duets in the bubble core (onebeing a source puck from a preceding duet and one being a reverse puckfrom a succeeding duet). The gum drop pairs are also referred to hereinby the Applicant by the terms “inner pairs.” The collective gum droppairs are referred to herein by the Applicant as a “bubble gum set.”Because the gum drop pairs are formed only within the bubble core, itcan be seen that two pucks, the first and last pucks in the bubble core,will not have an adjacent puck to be paired with to form a gum droppair, and therefore are not part of the bubble gum set.

For example, shown in FIG. 4Q is the bubble gum set comprising the gumdrop pairs for the first group as determined from the first group bubbleof FIG. 4P. The first gum drop pair of the bubble gum set shown in FIG.4Q is the pairing of the adjacent pucks in the first pair of adjacentduets in the bubble core, which is DA-DC (SP43-RP3). The following gumdrop pairs are BD-CB (SP42-RP4), CB-BA (SP41-RP5), and so on, and endswith the last gum drop pair of CA-BA (SP25-RP21). It can be seen thatthe first and last pucks in bubble core shown in FIG. 4P, which are AD(RP2) and AC (SP24) are not part of the bubble gum set.

The next stage of the super cooling process performed by the controlunit 18 involves a summarization technique. In the previous steps of thesuper cooling process discussed above, the relative order of entitieshas been generally maintained. In the following steps, the entities aresummarized. These summation entities result in an unorderedrepresentation of at least a portion of the input stream, containing inthem positional information.

Once the first group bubble has been formed in the step 82, the controlunit 18 branches to a summarization subroutine, which is shown in FIG. 3as a step 98. In general, in the summarization subroutine 98, the gumdrop pairs are summarized so as to represent the information therein ina more concise manner. To summarize the gum drop pairs, the set of gumdrop pairs are evaluated to determine how many gum drop pairs containthe same sequence of drops or symbols. For each unique sequence orcombination of drops within the set of gum drop pairs, which is alsoreferred to herein as a “gum drop pair type”, a count value is assignedrepresenting the number of gum drop pairs which contain that gum droppair type.

One embodiment of the summarization subroutine 98 is shown in moredetail in FIG. 10. In a first step 100 of the summarization subroutine98, the gum drop pairs in the first group bubble are defined as an “odd”or “even” depending on the placement or order of the gum drop pairwithin the bubble gum set of the first group bubble. For example, alsoshown in FIG. 4Q next to each gum drop pair is an odd/even assignmentfor purposes of illustration, wherein each of the odd gum drop pairs areidentified by the character “o” next to the gum drop pair, and each ofthe even gum drop pairs are identified by the character “e” next to thegum drop pair.

In a step 102 of the summarization subroutine 98, the odd set of gumdrop pairs are evaluated to determine how many gum drop pairs containthe same sequence of drops or symbols, i.e., have the same gum drop pairtype; and similarly the even set of gum drop pairs are evaluated todetermine how many gum drop pairs have the same gum drop pair type. Foreach unique gum drop pair type contained within the sets of odd and evengum drop pairs, a count value is assigned representing the number of gumdrop pairs which contain that gum drop pair type in both the odd set ofgum drop pairs and the even set of gum drop pairs. For example, shown inFIG. 4R is the odd set of gum drop pairs of FIG. 4Q for the first group,and the unique gum drop pair types from the odd set with the count ofgum drop pairs having that unique gum drop pair type. Below the odd setof gum drop pairs in FIG. 4R is the even set of gum drop pairs of FIG.4Q for the first group, and the unique gum drop pair types from the evenset with the count of gum drop pairs having that unique gum drop pairtype.

While the summarization subroutine 98 has been described above in oneembodiment as defining the gum drop pairs as odd or even in step 100 andthen determining gum drop pair types and counts for the odd and even setof gum drop pairs in step 102, it should be understood that the odd/evencharacterization of step 100 can be dropped and the gum drop pair typesand counts be determined for the collective set of gum drop pairs instep 102.

Also, the present invention contemplates that the gum drop pairs can besummarized and represented in a different manner. For example, it can beseen that there is a correspondence between adjacently disposed gum droppairs in that the second or right puck (i.e., the right pair of twosymbols or drops) of a preceding gum drop pair has a reverserelationship with the first or left puck (i.e., the left pair of twosymbols or drops) of a succeeding gum drop pair. For example, if theright puck of the preceding gum drop pair includes the symbols DC, whichrepresents the value 1110, the left puck of the succeeding gum drop pairincludes symbols which represent the reverse of that value, 0111, whichis BD.

To utilize this relationship between adjacently disposed gum drop pairs,the summarization subroutine 98 in one embodiment further includes astep 104 which takes the gum drop pairs resulting from the step 82 forthe first group bubble and represents them in a partial form, which isreferred to herein by the Applicant by the term “adjacent gum droppairs”. In general, to form each adjacent gum drop pairs in the step104, two consecutive and adjacently disposed gum drop pairs (one odd andone even) are taken together, which is referred to herein by theApplicant as a “fully qualified” representation of the gum drop pairs.Then, from the adjacent gum drop pairs, the repetitive information inthe preceding gum drop pair is omitted. The process of removing therepetitive information in the representation of two adjacently disposedgum drop pairs is referred to herein by the Applicant as a “partiallyqualified” representation of gum drop pairs.

For example, shown in FIG. 4S are the fully qualified adjacentlydisposed gum drop pairs for the first group of FIG. 4Q, and theresulting partially qualified adjacent gum drop pairs derived therefrom.The omitted puck in the adjacent gum drop pairs is represented by a “:”in FIG. 4S for purposes of illustration and clarity, however it shouldbe understood that the “:” has no other significance in regards thereto.The three remaining pucks of the adjacent gum drop pairs is referred toherein by the Applicant as a “triplet.” However, it should be understoodthat each of the adjacent gum drop pairs includes information indicativeof two gum drop pairs (one even and one odd), and thus is actuallyindicative of four pucks.

Once the partially qualified adjacent gum drop pairs for the first groupare formed in the step 104, the control unit 18 branches to a step 105,wherein the set of adjacent gum drop pairs are evaluated to determineany adjacent gum drop pairs which contain the same sequence of drops orsymbols, in a similar manner as discussed above for the gum drop paircounts. For each unique sequence of drops in the adjacent gum droppairs, which is referred to herein as an “adjacent gum drop pairs type”,a count value is assigned representative of the number of the adjacentgum drop pairs which contain that sequence. For example, also shown inFIG. 4S are the corresponding adjacent gum drop pairs types and countsfor the first group.

A final step 106 performed by the control unit 18 for the super coolingprocess for the first group is to derive a super cooled set for thefirst group, which represents a portion of the information within theoriginal input stream in a different form containing positionalinformation. In one embodiment, the super cooled set includes dataindicative of the following elements for the first group: 1) the totalnumber of droplets in the input stream, 2) the number of source pucks inthe first group, 3) the number of reverse pucks in the first group, 4)the bubble scum puck for the first group, 5) the starting or first gumdrop pair and the starting adjacent gum drop pairs in the bubble gum setfor the first group, 6) the ending or last gum drop pair and endingadjacent gum drop pairs in the bubble gum set for the first group, 7)the odd and even gum drop pair types and counts 8) the adjacent gum droppairs types and counts for the first group, 9) the inversion pucks (orduets) in the first group, and 10) the padding droplets (after spray).

For example, shown in FIG. 4T is an exemplary super cooled set for thefirst group. (Note that element ten is not applicable in the exemplarysuper cooled set since the exemplary input stream from which it isderived did not have any padding droplets, and is denoted as such inFIG. 4T by a “N/A” for purposes of illustration. Also, the parentheticalreferences in FIG. 4T are only included for purposes of illustration andclarity.)

In a similar manner as the first group, once the second group has beenformed in the step 64, the control unit branches to a step 110 as shownin FIG. 3, wherein the source pucks and the reverse pucks in the secondgroup are reordered to form an ordering referred to herein as a “secondgroup bubble”. Similar to the step 82 discussed above for the firstgroup bubble, to form the second group bubble in the step 110, the firstsource puck in the top segment of source pucks (or the bubble scum ofthe second group bubble) is followed by a plurality of pairings of eachsucceeding source puck in the top segment of source pucks with itscorresponding precedential reverse puck in the reverse ordered, bottomsegment of reverse pucks. These pairings are likewise referred to asduets, with the final pairings being inversion duets of the second groupbubble. The set of duets, excluding the inversion duets, is likewisereferred to as the bubble core of the second group bubble. Similarly, apairing of adjacent pucks in adjacent duets in the bubble core of thesecond group bubble (one being a reverse puck from a preceding duet andone being a source puck from a succeeding duet) is likewise referred toherein by the term “inner pair,” or “gum drop pair” and the collectivegum drop pairs of the second bubble group are referred to herein by theterm “bubble gum set” for the second group. Again, the first and lastpuck in the bubble core will be unpaired and are not be used to form agum drop pair.

For example, shown in FIG. 4U is an exemplary second group bubbleresulting from bubbling of the second group of FIG. 4O in a manner asdiscussed above, and shown in FIG. 4V is the bubble gum set comprisingthe gum drop pairs for the second group as determined from the secondgroup bubble of FIG. 4U.

Once the second group bubble has been formed in the step 110, thecontrol unit 18 branches to a summarization subroutine which is shown inFIG. 3 as a step 114. Once embodiment of the summarization subroutine114 for the second group, which is similar to the summarizationsubroutine 98 discussed above for the first group, is shown in moredetail in FIG. 11. In a first step 120 of the summarization subroutine114, the gum drop pairs in the second group bubble are defined as an“odd” or “even” depending on the placement or order of the gum drop pairwithin the bubble gum set of the second group bubble. For example, alsoshown in FIG. 4V next to each gum drop pair is an odd/even assignmentfor purposes of illustration, wherein each of the odd gum drop pairs areidentified by the character “o” next to the gum drop pair, and each ofthe even gum drop pairs are identified by the character “e” next to thegum drop pair.

In a step 122 of the summarization subroutine 114, the odd set of gumdrop pairs are evaluated to determine how many gum drop pairs containthe same sequence of drops or symbols, and similarly, the even set ofgum drop pairs are evaluated to determine how many gum drop pairscontain the same sequence of drops or symbols. For each unique sequenceof drops contained within the odd and even gum drop pairs, which is alsoreferred to herein as a “gum drop pair type”, a count value is assignedrepresenting the number of gum drop pairs which contain that gum droppair type in both the odd set of gum drop pairs and the even set of gumdrop pairs for the second group. For example, shown in FIG. 4W is theodd set of gum drop pairs of FIG. 4V for the second group, and theunique gum drop pair types from the odd set with the count of gum droppairs having that unique gum drop pair type. Below the odd set of gumdrop pairs in FIG. 4W is the even set of gum drop pairs of FIG. 4V forthe second group, and the unique gum drop pair types from the even setwith the count of gum drop pairs having that unique gum drop pair type.

While the summarization subroutine 114 has been described above in oneembodiment as defining the gum drop pairs as odd or even in step 120 andthen determining gum drop pair types and counts for the odd and even setof gum drop pairs in step 122, it should be understood that the odd/evencharacterization of step 120 can be dropped and the gum drop pair typesand counts determined for the collective set of gum drop pairs in step122.

Similar to the summarization subroutine 98 discussed above for the firstgroup, the summarization subroutine 114 for the second group in oneembodiment includes a step 124 wherein adjacent gum drop pairs areformed from the gum drop pairs of the second group. Then once theadjacent gum drop pairs for the second group are formed, the controlunit 18 branches to a step 126 wherein the set of adjacent gum droppairs are evaluated to determine the adjacent gum drop pairs types andcounts for the second group. For example, shown in FIG. 4X are theresulting fully and partially qualified adjacent gum drop pairs for thesecond group of FIG. 4V, and the corresponding adjacent gum drop pairstypes and counts.

As shown in FIG. 3, a final step 128 performed by the control unit 18for the super cooling process for the second group is to derive a supercooled set for the second group, which represents a portion of theinformation within the original input stream in a different form,containing positional information, in a similar manner as discussedabove in step 106 for the first group. In one embodiment, the supercooled set includes data indicative of the following elements for thesecond group: 1) the total number of droplets in the input stream, 2)the number of source pucks in the second group, 3) the number of reversepucks in the second group, 4) the bubble scum puck for the second group,5) the starting or first gum drop pair and the starting adjacent gumdrop pairs in the bubble gum set for the second group, 6) the ending orlast gum drop pair and the ending adjacent gum drop pairs in the bubblegum set for the second group, 7) the odd and even gum drop pair typesand counts for the second group, 8) the adjacent gum drop pairs typesand counts for the second group, 9) the inversion pucks (or duets) inthe second group, and 10) the padding droplets (after spray).

For example, shown in FIG. 4Y is a super cooled set for the secondgroup. (Note that element ten is not applicable in the exemplary supercooled set since the exemplary input stream from which it is derived didnot have any padding droplets, and is denoted as such by a “N/A” forpurposes of illustration. Also, the parenthetical references in FIG. 4Yare only included for purposes of illustration and clarity.)

It should be understood that while the super cooled sets for the firstand second groups have been described herein in one embodiment asincluding ten elements each, elements within the super cooled set forthe first group and for the second group (taken individually or incombination) which lend themselves to being repetitive, redundant, orotherwise unnecessary can be omitted accordingly (however redundancy canbe beneficial, such as for example for checking validity or to ensurestructural consistency between super cooled sets). For example, sincethe number of droplets in the input stream is already provided in thesuper cooled set for the first group, it may be omitted from the secondgroup. Further, elements that lend themselves to being derived from oneor more other elements can likewise be omitted accordingly since suchinformation can be obtained indirectly form the other elements. Further,while the super cooling process has been discussed in terms ofgenerating a super cooled set for the first group and a super cooled setfor the second group, it should be understood that the elements thereofmay be combined together and provided in a common super cooled set inaccordance with the present invention.

Once the super cooled sets are determined for the first group and secondgroup in the steps 106 and 128, respectively, the control unit 18outputs the super cooled sets so that the super cooled sets can beutilized (e.g., transmitted and/or stored).

The super cooled sets of the present invention can be outputted in itswhole form, which the Applicant refers to herein as being in an “openbox mode” representation of the input stream. This is the preferred modeof representing the input stream when the information within the inputstream is not sensitive to confidentiality or in the public domain.However, in instances where information is of a confidential orsensitive nature, each of the super cooled sets is “encrypted” by amethod referred to herein by the Applicant by the term “lock box mode.”Because the lock box mode can be applied similarly to any super cooledset, only the super cooled set for the first group is discussed infurther detail with reference to FIGS. 12A-12B for purposes of brevityand clarity.

The lock box mode consists of a “lock” component 170, a “key” component172 and a “combination” component 174, that when combined, provides thesuper cooled set in the open box mode. To “lock” the super cooled set soas put the super cooled set in the lock box mode, at least a portion ofthe super cooled set for the first group is divided into two parts, oneof which is used for forming the lock component 170 and one of which isused for forming the key component 172. In one embodiment, the adjacentgum drop pair types and counts of the super cooled set is the portion ofthe super cooled set which is divided into the two parts, as shown forexample in FIG. 12A. The division of the adjacent gum drop pairs typesand counts can be done in any manner, but are preferably divided so asto maximize bandwidth efficiency. A predetermined mathematical operationis then applied to the counts in each part, which results in the lockcomponent 170 and the key component 172. In one embodiment, as shown forexample in FIG. 12A, the mathematical operations are predeterminednumbers which are added to or subtracted from the adjacent gum drop paircounts.

The combination component 174 of the lock box mode is the reverse of themathematical operations applied to form the lock component 170 and keycomponent 172. Therefore it can be seen that to transform the supercooled set from the lock box mode to the open box mode, the combinationcomponent 174 (which reverses the mathematical operation for eachadjacent gum drop pair count) is applied to the lock component 170 andto the key component 172. The resulting adjacent gum drop pair counts inthe lock component 170 are then combined to the resulting adjacent gumdrop pairs counts in the key component 172 to obtain the full counts forthe adjacent gum drop pairs of the super cooled set for the first group.For example, shown in FIG. 12B is the combination component 174 beingapplied to the lock component 170 and key component 172 of FIG. 12A, andthe resulting super cooled set in the open box mode after the resultingadjacent gum drop pairs of the lock component 170 and the key component172 have been combined.

In the lock box mode, the lock component 170, the key component 172, andthe combination component 174 are preferably transmitted and/or storedapart so that there is no indication of the input stream beingrepresented by the super cooled set until the lock, key and combinationcomponents 170, 172 and 174 are combined to derive the super cooled setin the open box mode. Further encryption can result from the use ofmultiple lock components 170, key components 172, and/or combinationcomponents 174.

While the present invention is described in one embodiment as encryptingthe super cooled input stream set using the lock box mode fortransmission and storage, it should be understood that the presentinvention contemplates that any encryption technique known in the art orlater developed can be utilized during the transmission and/or storageof the super cooled input stream set in accordance with the presentinvention. Further, while only the adjacent gum drop pair counts havebeen discussed and shown by way of illustration as being modified in thelock box mode, it should be understood that the present inventioncontemplates that other information contained within the super cooledset can also be modified in the lock box mode.

It should be pointed out that the encoding technique containingpositional information of the present invention discussed herein isreally a summation process. Counts for each entity defined is in theform similar to the number system used in every day life where countsare expressed in the units ones, tens, hundreds, thousands, etc., torepresent the number of objects. This is normally recognized to be a“geometric” representation of the object counts. Therefore by inference,it should be pointed out that this method of summation leads to a“geometric” encoding of information with positional information implicitin it.

Due to the summarization technique of the super cooling process, thepresent invention allows for information to be present in the encodedand un-coded formats within a frame or fixed memory space (e.g., onemegabyte of storage). Along with the un-coded data in this frame, thesuper cooled sets may represent the en-coded data in some other frame,as shown for example in FIG. 13. Generally, the super cooled sets willrepresent the en-coded and summarized data in some other frame. Repeatedsuper cooling of data in a frame comprising the super cooled set fromthe previous or last cycle performed and the non-super cooled data inthe current frame (which is new data) is referred to herein by theApplicant by the term “super freezing”. This process can be repeatedad-infinitLlm to obtain a final super frozen set consisting of the firstgroup and second group super frozen sets (which is the same as a supercooled set for the final frame) from which all the frames can bederived. In essence what is accomplished is geometric encoding ofgeometrically compressed information leading to infinite compression.

In addition to the various processes described above, Applicant furtherpresents two other phenomena observed in relation to the super coolingprocess of the present invention. First, it should be noted that aspecial case arises in step 32 of the super cooling process if therippled input stream is rotated to the right in the formation of thesource stream, and the duplicate rippled stream is rotated to the leftin the formation of the reverse stream, by N positions (rather than N+1positions). In this case, the source and reverse pucks lose theirprecedence relationship and exhibit a “mirrored” relationship when theyare divided into the first group and second group in step 64, whereinthe source pucks and reverse pucks in the same position in theside-by-side comparison are evenly matched (with one exception in thesecond group: RP 43=AA-SP1=CA). Pucks that are in the same position andexhibiting the mirrored relationship are referred to herein by theApplicant as “twins”.

For example, shown in FIG. 14 is the resulting first group and thesecond group when the exemplary rippled input stream of FIG. 4C isrotated to the right by N droplet positions and the exemplary duplicaterippled stream (which is a duplicate of the rippled input stream of FIG.4B) is rotated to the left N droplet positions. The mirroredrelationships are indicated by a horizontal line drawn between thereverse pucks and source pucks in FIG. 14 for purposes of illustration.

With regard to the second observation, it was discussed above inreference to the super cooling process that the source pucks and thereverse pucks have a precedential reverse relationship when the top halfof the source pucks is compared side-by-side to the bottom half of thereverse pucks taken in reverse order, and the top half of the series ofreverse pucks is compared side-by-side to the bottom half of the sourcepucks taken in reverse order. The precedential reverse relationshiparises in that substantially each reverse puck in the top half ofreverse pucks has a value which is the reverse of the value of a sourcepuck located in a preceding position in the reverse ordered, bottom halfof source pucks; and substantially each source puck in the top half ofsource pucks has a value which is the reverse of the value of a reversepuck in the top half of reverse pucks. By taking the duets, which arethe pairs of reverse pucks and source pucks having the precedentialreverse relationship, it can be seen that the duets have a double helixarrangement, similar to that seen in DNA.

For example, shown in FIG. 15 is a subset of duets taken from theexemplary bubble core of duets of FIG. 4P for the first group. Next tothe subset of duets are two representations of the subset. In theleftmost representation of the subset, the reverse relationship betweendrops of the duets are shown by arrows drawn therebetween. Thenon-relationships (as between adjacent duets) are shown by the dottedlines drawn therebetween. If the arrows and the dotted lines are takento be part of the same line, they result in a double helix, as shown inthe rightmost representation of the subset. Applicant believes thisphenomenon explains how the double helix nature of the DNA structurecomes about.

It is Applicant's belief that the bubble groups of the super coolingprocess of the present invention is the same as DNA, but in a slightlydifferent mold. To see how the arrangement of drops from the exemplarysubset of duets of FIG. 15 relates to the double helix arrangement ofDNA, a transformation process is applied to the subset of duets, asshown in FIGS. 16A-16B and as discussed further below. The Applicantbelieves that the reason for this modification is the nature ofreplication associated with DNA. The rightmost structure of FIG. 15 doesnot lend itself to easy replication.

Shown in FIG. 16A is the subset of duets in the different stages of thetransformation process, as will be discussed further below withreference to FIG. 16B. In FIG. 16A, the subset of duets is shown first.Shown next thereto is a representation of a first double helix structure(as indicated by the vertical and horizontal lines) for the subset ofduets after the first step of the transformation (labeled as process550) is applied. Then shown is a second double helix structure using asingle tier encoded representation of the subset of duets using thefirst helix and resulting in the second helix structure from the nextstep of the transformation process (labeled as process 554), followed bya two tier encoded DNA representation with the first helix and thesecond helix resulting from the last step of the transformation process(labeled as process 558).

Note that the letters “A”, “B”, “C”, and “D” are used in the DNArepresentation here. They map to the common DNA sequence letters “A”,“C”, “G”, and “T” although not necessarily on a one-to-one basis.

The transformation process applied to the subset of duets is shown in ageneral flow diagram in FIG. 16B, with an example shown below whereinthe first duet of the subset of duets is shown during each step of thetransformation process for purposes of illustration. From theillustration of the transformation process for the first duet, oneskilled in the art will understand how to apply the transformationprocess to the other duets.

As shown in FIG. 16B, in a step 550 of the transformation process, thedrops in the bottom or second puck in the duet are swapped or reversedin order. For example, as shown in FIG. 16B for the first duet, thebottom puck is the source puck DA. After swapping the drops in thebottom puck, the bottom puck of the duet now has a value of AD (as alsoshown in FIG. 16A). In a step 554, the set of four drops in the duet atthis point are then rotated counter-clockwise by one position or ninetydegrees. For example, as shown in FIG. 16B, the result of rotating theset of four drops in the duet is a top “puck” with a value DD and abottom “puck” with a value AA (as also shown in FIG. 16A). In a step558, the drops at this point are then converted from single tierencoding to two-tier encoding. For example, as shown in FIG. 16B, theresult of converting the drops from single tier encoding to two-tierencoding is a top “puck” with a value DA and a bottom “puck” with avalue AD (as also shown in FIG. 16A). Each of the resulting “pucks” ofthe transformation process is referred to herein by the Applicant as a“DNA pair”.

Thus it can be seen that the reverse of the transformation processapplied to two adjacent DNA pairs yields the duets of the bubble core.In other words, by taking two adjacent DNA pairs, converting the DNApairs to single tier encoding, rotating the DNA pair values clockwise byninety degrees, and reversing the order of the bottom pair, the duetvalues result and can be subsequently decoded into an ordered binarystream by reversing the steps recited above for encoding the orderedbinary stream into the DNA pair values. Therefore, Applicant believesthat one application of the present invention is its use in convertingthe helix structure of DNA into a binary sequence so as to retrieve adata stream in the form of 0's and 1's which represents the informationcontained in the DNA structure.

Further, the Applicant believes that if the DNA sequence has strictlysequenced information and their summarized values are to be found in thestem cell set, then transforming the DNA to a binary sequence of valuesand super cooling it would yield information that closely corresponds tothose facets of the stem cell set which are represented in the DNA. Fromthis established correspondence, it should be possible to derive thebinary sequence of those features of the stem cell set which are notrepresented in the DNA, such as the regeneration of most organs.

From the above description, it is clear that the present invention iswell adapted to carry out the objects and to attain the advantagesmentioned herein, as well as those inherent in the invention. Althoughthe foregoing invention has been described in some detail by way ofillustration and example for purposes of clarity of understanding, itwill be apparent to those skilled in the art that certain changes andmodifications may be practiced without departing from the spirit andscope of the present invention, as described herein. Thus, the presentinvention is not intended to be limited to the embodiment shown but isto be accorded the widest scope consistent with the principles andfeatures described herein.

What is claimed is:
 1. A method for encoding an ordered binary stream,the method comprising the steps of: converting the ordered input binaryinto an ordered input quad stream by taking two adjacent binary valuesto form drops; and using encoding on drops to form the ordered inputquad stream.
 2. The method of claim 1, wherein the step of encoding isdefined further as encoding the drops into a single tier format.
 3. Themethod of claim 2, wherein the binary stream in the single tier formatis taken as a whole.
 4. The method of claim 1, wherein the step ofencoding is defined further as encoding the drops into a two-tierformat.
 5. The method of claim 4, wherein the two-tier format includesan odd component and an even component.
 6. A method for encoding anordered binary input stream, comprising the steps of: analyzing thelength of the ordered binary input stream to determine whether thenumber of digits in the ordered binary input stream is an odd multipleof four; and appending the ordered binary input string with a number ofdigits sufficient to increase the length of the ordered binary inputstream to a number of digits that is an odd multiple of four.
 7. Themethod of claim 6, further comprising the step of inserting alternately0's and 1's starting with either a “0” or a “1” into the ordered binaryinput stream, after the binary strings have been appended thereto, aftereach binary value of the ordered input stream to obtain a rippled binarystream retaining the original order of the ordered binary input stream.8. The method of claim 7, further comprising the steps of: copying therippled binary stream to form two identical rippled binary streams;rotating one of the rippled binary streams to the right a number ofpositions to produce a source stream; and rotating the other one of therippled binary streams to the left the same number of positions andreversing the rippled binary stream that has been previously rotated tothe left to form a reverse stream.
 9. The method of claim 8, furthercomprising the step of converting the source and reverse binary streamsinto quad streams by representing each adjacent pair of bits by a letterindicative of the value of the adjacent pair.
 10. The method of claim 9,wherein adjacent letters in the quad streams are characterized as dropsand wherein adjacent drops form drop pairs representative of the sourcestream and reverse stream with the ordering of the drop pairs in thesource stream and reverse stream representing positional informationwith respect to the original binary input stream.
 11. The method ofclaim 10, further comprising the step of dividing each of the source andreverse streams into substantial halves to form a top half and a bottomhalf of the source stream, and a top half and a bottom half of thereverse stream; such that the top half and the bottom half of each ofthe source and reverse streams includes at least one drop pair havingsame drop values.
 12. The method of claim 11, further comprising thestep of forming two segments, one of the segments comprising the tophalf of the source stream and the bottom half of the reverse stream, andthe other one of the segments comprising the top half of the sourcestream and bottom half of the reverse stream.
 13. The method of claim12, further comprising the step of indexing, in one of the segments, thetop half of the source stream and the bottom half of the reverse streamin a side-by-side relationship such that the drop pairs in the top halfof the source stream have a same but reverse relationship to the droppairs in the bottom half of the reverse stream.
 14. The method of claim13, further comprising the step of indexing, in the other one of thesegments, the bottom half of the source stream and the top half of thereverse stream in a side-by-side relationship such that the drop pairsin the bottom half of the source stream have a same but reverserelationship to the drop pairs in the top half of the reverse stream.15. The method of claim 14, further comprising the step of merging thedrop pairs in the segments such that the drop pairs having aside-by-side relationship form duets having the same binary values butreversed in order.
 16. The method of claim 15, wherein the resultantmerged drop pairs form a “bubble”, and wherein the bubble includes afirst drop pair which is unpaired, followed by a series of duets to forma “bubble core”.
 17. The method of claim 16, wherein a second drop pairof a top most duet and a first drop pair of a second duet form anadjacency relationship to form adjacent gum drop pairs; the set of alladjacent gum drop pairs together with the top most drop pair and thebottom most drop pair of the bubble core, and the unpaired first droppair represent the binary input stream.
 18. The method of claim 15,wherein the duets of the bubble core exhibit a property commonlyunderstood as a double helix DNA sequence.